Tens of thousands of Spaniards have taken to the streets of Madrid in a show of force against government plans to roll back access to abortion in the country.

Waving homemade signs with messages such as "My ovaries: not those of priests, nor of politicians", the crowd chanted and whistled as it snaked its way through central Madrid on Saturday. Police said more than 15,000 had turned out.

"We are here to protest against a government that wants to take us back to the times of Franco," said one demonstrator, Manuel Navarro. "We are stepping backwards with this law."

In late December the governing People's party approved legislation that would severely curtail access to abortion in the country. Since 2010, women in Spain have had the right to an abortion until the 14th week of pregnancy. In cases where the mother's health is at risk or when the foetus shows serious deformities, Spanish women can terminate the pregnancy until the 22nd week. Under the new measures put forward by the government, abortions in Spain would only be allowed in the case of rape or when there is a risk to the physical or mental health of the mother. Women wanting abortions will need the approval of two medical professionals to prove these circumstances.

Carmen Veiga was almost in tears as she surveyed the large crowd. During the holidays, she and a few other women in the northern Spanish city of Gijón had come up with the idea of travelling to Madrid to deliver a letter to the government demanding that it abandon the legislation. Seats on their "freedom train" were filled within days, prompting other towns and cities across the country to do the same.

The result, said Veiga, was a coming together of protest movements from across the country and the strongest show of force seen since the government announced the measures just over a month ago. "It is incredible to see all these people come together to defend women's rights," she said. "And it's necessary – what they're trying to do is a brutal reversal of women's rights."

More than 300 groups worked to organise the protest, and it showed in the variety of the attendees, who ranged from toddlers to senior citizens. Women's groups pointed out that thousands of men had joined the protest.

"This law affects us just as much – we're parents too," said Rodrigo Martínez Barrios, 20. "To me, this sounds like a return to the Middle Ages." He was also suspicious of the timing of the bill. "Politicians are using this issue to distract us from the bigger issues – the corruption, the crisis, the economy of this country."

One woman said she had woken up at 5am to make the 280-mile journey from Santander to Madrid. Carmen, who did not want to give her last name, looked around nervously before leaning in to explain why it was so important that she be here today.

"This is my fight," she said, her voice shaking. Thirty years earlier, she had travelled to London for an abortion. "I didn't speak a word of English. But I didn't know what else to do." A condom had broken and they knew they could not afford to raise a third child.

"It was heartbreaking. And it was even worse that I had to leave my country to do it or risk going to jail." She and her husband scraped together whatever money they could, draining their life savings to send her to London alone. "I am here today because I never want my grandchildren to go through that," said the 63-year-old.

Her voice rose as she added: "It can't be that after 30 years we're back in the same situation. That means we're not advancing as a country."

The proposed measures come as statistics show that the number of abortions in Spain is on the decline. Nonetheless, the changes are being championed by the Roman Catholic church – a powerful force in a country where 70% of the population say they are Catholic. "The church wants to return to a time when they controlled us, when they suffocated us. They want to take us backwards," said protester Mercedes López.

The People's party has said repeatedly that the scaling back of abortion laws was an election promise that it must now fulfil. As polls show that between 70% and 80% of Spaniards are against the changes, the party's stance has put it at odds with its electorate.

Recent weeks have seen prime minister Mariano Rajoy soften his stance on the bill. "The constitution and different opinions will be taken into account," he told parliament last week. The Spanish congress, in which the People's party holds a strong majority, is expected to pass the bill in late spring.